Answer:
add them then multiply
Step-by-step explanation:
you solve it like an equation.
4x+20<40
4x<20
x<5
so the answer would be anything less than 5, which is A
Answer:
0.200
Step-by-step explanation:
∑ₓ₌₁⁴⁰ (1 + i)⁻ˣ = 5
∑ₓ₌₁⁴⁰ ((1 + i)⁻¹)ˣ = 5
This is a geometric series. The sum of the first n terms of a geometric series is:
S = a₁ (1 − rⁿ) / (1 − r)
where a₁ is the first term and r is the common ratio.
Here, a₁ = (1 + i)⁻¹, r = (1 + i)⁻¹, and n = 40. For simplicity, let's write both a₁ and r in terms of r. So a₁ = r and r = r.
5 = r (1 − r⁴⁰) / (1 − r)
5 (1 − r) = r (1 − r⁴⁰)
5 − 5r = r − r⁴¹
r⁴¹ − 6r + 5 = 0
Solving with a calculator, r ≈ 0.8334.
Therefore:
(1 + i)⁻¹ = 0.8334
1 + i = 1.200
i = 0.200
These are the steps:
1. Find the area of the trapezium {Whole figure).
2. FInd the area of the rectangle (unshaded).
3. Area of the shaded = Area of trapezium - Area of the rectangle.
<u>Step 1: Find the area of the trapezium</u>:
Formula : Area of trapezium = 1/2 (a + b)h
Area = 1/2 ( 25 + 15) (12) = 240 yd²
<u>Step </u><u>2 :</u><u> Find the area of the rectangle</u>:
Formula : Area = Length x Width
Area = 12 x 3 = 36 yd²
<u>Step 3: Find the shaded region:</u>
240 - 36 = 204 yd²
Answer: 204 yd²